# Two trains X and Y travelling in the same direction cross each other in 120 seconds. The speed of train Y is 50% of the speed of train X. If speed of

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Two trains X and Y travelling in the same direction cross each other in 120 seconds. The speed of train Y is 50% of the speed of train X. If speed of train Y increases by 10 m/s, it would take 60 seconds to cross a platform of length 300m. Train X would cross the platform of length 300 m in 30 seconds. Find the speed of train X.
1. 80
2. 76
3. 85
4. 79

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Correct Answer - Option 1 : 80

Given:

Two trains X and Y travelling in the same direction cross each other in 120 seconds. The speed of train Y is 50% of the speed of train X. If speed of train Y increases by 10 m/s, it would take 60 seconds to cross a platform of length 300m. Train X would cross the platform of length 300 m in 30 seconds.

Formula:

If the lengths of two trains are a and b,

Time taken to cross each other when travelling in same direction = (a + b)/(va - vb)

Time taken to cross each other when travelling in opposite direction = (a + b)/(va + vb)

where va and vb are the speeds of trains A and B respectively.

Calculation:

Let the lengths of X and y be lx and ly respectively.

Let the speeds of X and Y be 2v and v respectively.

(lx + ly)/v = 120

⇒ (ly + 300)/(v + 10) = 60

⇒ (lx + 300)/(2v) = 30

Solving, we get,
⇒ lx = 2100,

⇒ ly = 2700

⇒ v = 40

Speed of train X = 2v = 80 m/s